?? where a maximal parabolic subalgebra (for example ...) lives ... ??? "co-weight space" ??? .... cocone therein ... ???? ..... ??? dual to cone where corresponding extremal weight lies .... ???? ..... ?? more generally, higher dimensional wall of weyl chamber as cone dual to non-maximal parabolic subalgebra .... kaleidoscope-as-fan toric variety ... ??? .... conceptual / geometric interpretation ... ??? ....